[1]董云达,尤燕飞..Richardson迭代法的一个常数步长[J].郑州大学学报(工学版),2009,30(03):139-140.
　DONG Yunda,YOU Yanfei.Constant Step Length in Richardson Iterative Method[J].Journal of Zhengzhou University (Engineering Science),2009,30(03):139-140.
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Richardson迭代法的一个常数步长()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
30
期数:
2009年03期
页码:
139-140
栏目:
出版日期:
1900-01-01

文章信息/Info

Title:
Constant Step Length in Richardson Iterative Method
作者:
董云达; 尤燕飞.
郑州大学,数学系,河南,郑州,450001, 南京大学,数学系,江苏,南京,210093
Author(s):
DONG Yunda; YOU Yanfei
(I．Department of Mathematics，Zhengzhou University，Zhengzhou 450001，China；2．Department of Mathematics，Nanjing University，Nanjing 210093，China
关键词:
正定线性方程组;  Richardson迭代法;  步长;  收敛
Keywords:
systems of positive definite linear equations;  Richardson iterative method;  step size;  Convergence
文献标志码:
A
摘要:
对于求解对称正定线性方程组的Richardson迭代法,给出一个新的常数步长.它仅依赖于系数矩阵的对角线上的最小元素和最大特征值.而且,还证明了在该步长下Richardgon迭代法产生的梯度模序列线性地趋于0.初步的数值试验表明了新步长的某些优势.
Abstract:
Richardson iterative method for solving system of linear equations with the positive definite coeffi—cient matrix is considered，and a new constant step length rule only depending on the minimal diagonal elementand the maximum eigenvalue is proposed．Furthermore，the linear convergence of the generated gradient normsto zero is proved．Preliminary numerical tests show that the new rule is competitive for certain problems．
更新日期/Last Update: 1900-01-01